Abstract: A method of determining a configuration of a projection system for a lithographic apparatus as an implementation of a quadratic programming problem with a penalty function. The method includes: receiving dependencies of one or more optical properties of the projection system on a configuration of a plurality of manipulators of the projection system; receiving a plurality of constraints which correspond to physical constraints of the manipulators; finding an initial configuration of the manipulators; and iteratively finding an output configuration of the manipulators. The iteration includes repeating the following steps: determining a set of the plurality of constraints that are violated; determining an updated configuration of the manipulators, the updated configuration of the manipulators being dependent on the set of the plurality of constraints that are violated and a penalty strength; and increasing the penalty strength. These steps are repeated until a convergence criterion is met.

Abstract: A method of determining a configuration of a projection system for a lithographic apparatus as an implementation of a quadratic programming problem with a penalty function. The method includes: receiving dependencies of one or more optical properties of the projection system on a configuration of a plurality of manipulators of the projection system; receiving a plurality of constraints which correspond to physical constraints of the manipulators; finding an initial configuration of the manipulators; and iteratively finding an output configuration of the manipulators. The iteration includes repeating the following steps: determining a set of the plurality of constraints that are violated; determining an updated configuration of the manipulators, the updated configuration of the manipulators being dependent on the set of the plurality of constraints that are violated and a penalty strength; and increasing the penalty strength. These steps are repeated until a convergence criterion is met.

Abstract: A method of determining a configuration of a projection system for a lithographic apparatus, wherein manipulators of the projection system manipulate optical elements so as to adjust its optical properties, the method comprising: receiving dependencies of the optical properties of the projection system on a configuration of the manipulators, receiving a plurality of constraints of the manipulators, formulating a cost function, wherein the cost function represents a difference between the optical properties of the projection system for a given configuration of the manipulators and desired optical properties, wherein the cost function is formulated using the dependency of the optical properties on the configuration of the manipulators, scaling the cost function into a scaled variable space, wherein the scaling is performed by using the plurality of constraints and finding a solution configuration of the manipulators which substantially minimizes the scaled cost function subject to satisfying the plurality of co

Abstract: A method of determining a configuration of a projection system for a lithographic apparatus, wherein manipulators of the projection system manipulate optical elements so as to adjust its optical properties, the method comprising: receiving dependencies of the optical properties of the projection system on a configuration of the manipulators, receiving a plurality of constraints of the manipulators, formulating a cost function, wherein the cost function represents a difference between the optical properties of the projection system for a given configuration of the manipulators and desired optical properties, wherein the cost function is formulated using the dependency of the optical properties on the configuration of the manipulators, scaling the cost function into a scaled variable space, wherein the scaling is performed by using the plurality of constraints and finding a solution configuration of the manipulators which substantially minimises the scaled cost function subject to satisfying the plurality of co